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The Mathematical Mechanic by Mark Levi

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APPENDIX

PHYSICAL BACKGROUND

This short appendix contains the physical toolbox used throughout the book.

A.1 Springs

The toolbox for our thought experiments includes two types of springs: linear springs and constant tension springs.

Zero-length springs. A zero-length spring is the one whose tension is directly proportional to its length: stretching such a string to a length x requires the force kx. Here k is a constant (called the Hooke’s constant) that characterizes a particular spring. A small k means a lax spring, while a large k means a stiff spring. Note that the unstretched length of such a spring is zero.

POTENTIAL ENERGY OF A ZERO-LENGTH SPRING. By the definition, the potential energy of a spring is the work required to stretch the spring ...

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